I can't decide where, in our battle with the bedbugs, we reached the nadir. Was it when my son's reception class teacher called my wife to express her concern about the number of bites on his arms, body and face? "He says they're ... bedbug bites," she said, disbelievingly. "That's right," my wife replied. "We've got an infestation that we're being treated for." "Oh, I understand - I've come across bedbugs, when I've been travelling in Africa." The words "but not when I've been teaching in north London" went unspoken.

Was it when, for four nights running, our eight-year-old daughter kept us awake with her star-shaped sleeping position, because she was too afraid to sleep in her own bed after having awoken to see a pair of bedbugs lazing on her pillow?

Or was it when, a fortnight after we'd had the house chemically treated, I laboriously took apart the wooden frame of her bunk bed? I had spread white sheets across the floor, so I could see what fell out of the nooks and crannies of the frame, and by the end of the process the sheets were streaked red with blood from the 40 or so live and well-fed bugs I had squashed. My daughter marvelled at how much blood came out of each bug. I didn't have the heart to tell her where the blood had come from.

At this point, you're probably thinking that our house must be a vile hovel. You're probably right. It has all seemed a bit 14th century this past month, what with the bedbugs, the mice and the clothes moths. But be warned: we are not unusual. Bedbugs are on their way back, despite having been all but eradicated in the developed world by the 1980s.

In the US, in the postwar years, DDT was used to kill them off. In this country - what an English solution - the authorities shamed the population into seeking their own treatment, by drawing a link between infestation and slovenliness, thus establishing a stigma that survives today. In fact, your cleanliness or otherwise makes no difference to whether bedbugs set up home with you. All they're interested in is your blood. If you encounter them, there's a decent chance they're coming home with you. And you stand a decent chance of encountering them.

Stuart Hine, an entomologist at the Natural History Museum in London, estimates that there has been a threefold increase in London's bedbug population this decade. That figure is backed by the research of Bedbugs Limited, an extermination company founded by microbiologist David Cain after he became obsessed with the creatures.

No one is exactly sure how prevalent bedbugs are, though. There is no requirement to report infestations, and though many people do call their council's pest control department when they find them, different councils record reports in different ways. Cain used the Freedom of Information Act to request London borough council records of bedbugs. At the broadest level - borough by borough - the data offers little help. It's only when broken down almost street by street that patterns emerge: a corridor of bedbug infestation running from Elephant and Castle to Lewisham in south London, or corridors running from Gatwick and Heathrow to central London.

So why are the bedbugs biting? What brought them back to Britain? The simplest explanation is globalisation. Bedbugs are hugely effective hitchhikers: if you sleep in an infested room, they may climb into your luggage, or into your clothes. When you get home, they disembark and set up home in the darkest nooks of your bedroom, coming out in the hours before dawn to suck blood from your slumbering body. With more and more of us travelling abroad to regions where bedbugs were never eradicated, more and more of us are likely to bring them back. They thrive in homes inhabited by large numbers of people, where they are able to feed and breed freely.

We realised we had a bedbug problem just after Christmas. My wife came downstairs with a small insect - rust coloured, with a flat, oval body, a few millimetres in length - in a bowl. "This bug was crawling about on the bunk beds," she said. "What do you think it is?" Within 20 seconds, Google Images had supplied the answer.

In fact, the warning signs had been apparent for a while, we just hadn't seen them. Before Christmas our son had a perplexing rash on his leg that wouldn't clear up and the doctor had suggested it was an allergy. His room turned out to have relatively few bugs, while our daughter's had a much more severe infestation - yet we never saw a mark on her skin. Many people, it transpires, don't react to bites and so don't realise they have a problem until they find a live bug. The real eye-opener, though, was what the exterminator pointed out when he came round. At virtually all the joins in the wooden frame of the bunk beds were little black dots, as if the tips ballpoint pens had been tapped against the wood. Those black marks turned out to be bedbug faeces.

Where did we get our bugs? The exterminator estimated our house had been occupied for five months, which - to my mind - suggested we'd picked them up from a holiday house in France in the summer. Certainly, I remembered being bitten one night there, when I had been certain there was no mosquito in the room. But the exterminator reckoned we'd got them from public transport. That, he told us, is where most people pick up bedbugs. It's simple logic really: a vast number of people, including plenty who have returned from abroad (think about those corridors of infestation from the London airports into the city), offering bedbugs an array of hosts. But the transport companies are hardly at fault. Do we expect them to frisk every traveller for bedbugs? Could they check every bus and every train every night for bedbugs? That is what it would take to get the transport system clear. In the meantime, David Cain has a piece of advice for commuters: "Don't sit down on public transport."

When the exterminator had treated our kids' rooms, he left us with a lengthy manual of instructions. The kids needed to stay in their rooms because if the bugs' food source was removed, they would just infest new rooms. We were to examine the beds every day for living and dead bugs, and after two weeks we were to "deep clean" their rooms in the hope of eradicating the last stragglers. That fortnight seemed to last for ever. It was during that time that our son's teacher made the call that shamed us. It was on the last day of the fortnight that I took apart the bunk beds to find them crawling with living bugs. Even after the deep clean - performed by a woman who advised us that, in addition to never sitting down on public transport, we should always remove our clothes before entering a bedroom - we still needed another chemical treatment. That took place last week. We are praying that by next week we are clear - so we can get back to killing the mice.

So does no one have a good word for the bedbug? Even Stuart Hine, who - being an entomologist - says he can appreciate the beauty of every insect, can find nothing to admire. David Cain expresses grudging respect for their ability to thrive alongside humans for thousands of years, despite our best efforts. But I will stick up for these banes of my life. Among the things I have discovered is that the bedbug has a unique style of mating, known as traumatic insemination, in which the male simply stabs his sperm into the female's body cavity, bypassing her genitals. Professor Mike Siva-Jothy of Sheffield University has discovered that there is a "25% reduction in female lifespan" as a result - a surprisingly low figure. Siva-Jothy believes a unique organ, the spermalege, which protects the females, could in future help scientists produce a drug that reduces the transmission of diseases. There's more: what does a well-fed bedbug contain? Human blood. Some criminologists believe that scouring crime scenes for live bedbugs could provide investigators with a source of DNA. I'm not saying I won't be glad when ours are gone. But I have a little more sympathy for them than I did a month ago.

How to spot an infestation

• Look for unexplained rashes, although one in 10 people doesn't respond to bites. If you react badly, use antihistamines.

• Check your bedframe, or the joints of furniture, for black dots of between 0.5mm and 1mm - bedbug faeces. Contrary to myth, bedbugs do not live in your mattress, although they may be found in the seams.

• Check your sheets for bloodstains: you may have rolled over and crushed a bug after it has fed on you.

• If you have a severe infestation, you might notice a sweet, musty smell around your bedframe.

What to do if you're infested

• Call a professional extermination firm, and check its credentials. Many pest-control companies have diversified into bedbug control without any expertise. Following the advice of one company's website, we put grease-lined tins around our bed legs (to prevent bugs crawling up them). The exterminator guffawed at our stupidity. Don't try to kill the bugs yourself: last year an American woman blew up her home by lighting several insecticide "foggers" simultaneously: the propellant caused her gas supply to ignite. Don't use an aerosol-based insecticide, either: you'll kill some, but the fit ones will simply flee to another room.

• Don't throw away your furniture. The chances are that you will spread the bugs through your home.

• Talk to your neighbours. It's possible your bugs have come from them, or that you have given them yours. One of David Cain's customers reported a recurring infestation. He was being reinfested by a neighbour, whose property was home to an estimated 150,000 bedbugs (the average infestation is around 100).

• Don't panic. Bedbugs don't carry diseases, and their presence does not make you unclean.